i know that toilets do this kind of delayed start to flush when they are insufficiently vented. It happened to me when I was remodeling and for several months i had disconnected ALL the vents in my space. Also, I looked in to this subject a lot before and after, since i had a very complex plumbing situation that conditioned my remodel. So I think i know that a lack of venting will cause very slow draining that eventually speeds up. Some people like for their toilet to do this, as it increases the suction once it finally gets going.

So, if i were there, and if i owned the house, and if your description is exactly as i would describe it, then that is my first hypothesis. I.e. that there is not enough venting. Furthermore, your last sentence sounds to me like you have a slight backwards slope on the big pipe; if so, this reduces the amount of air that can flow back through the pipe when waste water is flowing out, same impact as if the pipe were smaller in diameter. That also has the same effect as insufficient venting, and it aggravates the problem, and this helps explain why the shower pan builds up so much water first before finally you get a good head of pressure and inertia and the water starts to flow rapidly.

What happens when you open all windows? What happens when you close all windows, doors, dryer vents, kitchen vents, and other places where outside air can get in? I'll bet that the shower drain holds back even longer before draining, and the flow is a lot slower when it does start draining, since there is no source of make-up air to replace the volume that the water takes up.